poj2155--Matrix（二维树状数组）

Given an N*N matrix A, whose elements are either 0 or 1. A[i, j] means the number in the i-th row and j-th column. Initially we have A[i, j] = 0 (1 <= i, j <= N). 

We can change the matrix in the following way. Given a rectangle whose upper-left corner is (x1, y1) and lower-right corner is (x2, y2), we change all the elements in the rectangle by using "not" operation (if it is a ‘0‘ then change it into ‘1‘ otherwise change it into ‘0‘). To maintain the information of the matrix, you are asked to write a program to receive and execute two kinds of instructions. 

1. C x1 y1 x2 y2 (1 <= x1 <= x2 <= n, 1 <= y1 <= y2 <= n) changes the matrix by using the rectangle whose upper-left corner is (x1, y1) and lower-right corner is (x2, y2). 
2. Q x y (1 <= x, y <= n) querys A[x, y]. 

The first line of the input is an integer X (X <= 10) representing the number of test cases. The following X blocks each represents a test case. 

The first line of each block contains two numbers N and T (2 <= N <= 1000, 1 <= T <= 50000) representing the size of the matrix and the number of the instructions. The following T lines each represents an instruction having the format "Q x y" or "C x1 y1 x2 y2", which has been described above. 

For each querying output one line, which has an integer representing A[x, y]. 

There is a blank line between every two continuous test cases. 

1
2 10
C 2 1 2 2
Q 2 2
C 2 1 2 1
Q 1 1
C 1 1 2 1
C 1 2 1 2
C 1 1 2 2
Q 1 1
C 1 1 2 1
Q 2 1

1
0
0
1

POJ Monthly,Lou Tiancheng

二维的树状数组，一般的修改和查询

对二维的树状数组的修改

void add(int i,int j,int d,int n)
{
    int x , y ;
    for(x = i ; x <= n ; x += lowbit(x))
        for(y = j ; y <= n ; y += lowbit(y))
            c[x][y] += d;
}

查询

int sum(int i,int j)
{
    int a = 0 , x , y ;
    for(x = i ; x >= 0 ; x -= lowbit(x))
        for(y = j ; y >= 0 ; y -= lowbit(y))
            a += c[x][y] ;
    return a ;
}

题意：给出n*n的矩阵，矩阵中的值只能为0或者1，初始值全部是0，C x1 y1 x2 y2 表示在（x1,y1）和(x2,y2)围成的矩形中的所有值变换 ；Q x y 查询该点当前的值，也可以认为是统计该点经过了几次的变化；

在这个题中树状数组由后向前更新，每一个点的值表示由该点向前的所有点变换的次数

对于C的操作

首先 将(1,1)到（x2,y2）的所有点+1 ，代表有该点向前的矩形中的变化次数均+1；再由 (x1-1,y2)(x2,y1-1)均-1，(x1-1,y1-1)+1，平衡掉多操作的点，那么当计算该点变换次数时，由该点向后累加，得到的总和就是该点的变换次数，如果是奇数代表1，否则是0.

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int c[1010][1010] ;
int lowbit(int x)
{
    return x & -x ;
}
void add(int i,int j,int d)
{
    int x , y ;
    for(x = i ; x > 0 ; x -= lowbit(x))
        for(y = j ; y > 0 ; y -= lowbit(y))
            c[x][y] += d;
}
int sum(int i,int j,int n)
{
    int a = 0 , x , y ;
    for(x = i ; x <= n ; x += lowbit(x))
        for(y = j ; y <= n ; y += lowbit(y))
            a += c[x][y] ;
    return a ;
}
int main()
{
    int t , tt , i , j , n , m , x1 , y1 , x2 , y2 ;
    char ch ;
    scanf("%d", &t);
    for(tt = 1 ; tt <= t ; tt++)
    {
        scanf("%d %d", &n, &m);
        memset(c,0,sizeof(c));
        while(m--)
        {
            getchar();
            scanf("%c", &ch);
            if( ch == 'C' )
            {
                scanf("%d %d %d %d", &x1, &y1, &x2, &y2);
                add(x2,y2,1);
                add(x1-1,y2,-1);
                add(x2,y1-1,-1);
                add(x1-1,y1-1,1);
            }
            else
            {
                scanf("%d %d", &x1, &y1);
                printf("%d\n", sum(x1,y1,n)%2 );

            }
        }
        if(tt != t)
            printf("\n");
    }
    return 0;
}